Let $r,c,sin{1,2,ldots,n}$ and let $P$ be a partial latin square of order $n$ in which each nonempty cell lies in row $r$, column $c$, or contains symbol $s$. We show that if $notin{3,4,5}$ and row $r$, column $c$, and symbol $s$ can be completed in $P$, then a completion of $P$ exists. As a consequence, this proves a conjecture made by Casselgren and H?ggkvist. Furthermore, we show exactly when row $r$, column $c$, and symbol $s$ can be completed.
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机译：设$ r，c，s in {1,2， ldots，n } $，并使$ P $为阶数为$ n $的部分拉丁方，其中每个非空单元格位于行$ r $的列中$ c $，或包含符号$ s $。我们显示如果$ n notin {3,4,5 } $和行$ r $，列$ c $和符号$ s $可以在$ P $中完成，则存在$ P $的完成。结果，这证明了Casselgren和H？ggkvist的猜想。此外，我们确切显示了何时可以完成行$ r $，列$ c $和符号$ s $。
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